Question

Lifetimes of a certain brand of lightbulbs is known to follow a right-skewed distribution with mean 24 months and standard deviation 2 months. Let X̄ represent the sampling distribution of the sample mean corresponding to a sample of size 1500 from this distribution. We expect this sampling distribution to be...

Select one:

a. Approximately Normal with a mean of 24 months and a standard deviation of 0.0013 months.

b. Right-skewed with a mean of approx. 24 months and a standard deviation of approx. 0.0516 months.

c. Right-skewed with a mean of approx. 24 months and a standard deviation of approx. 2 months.

d. Approximately Normal with a mean of 24 months and a standard deviation of 0.0516 months.

e. Approximately Normal with a mean of 24 months and a standard deviation of 2 months.

Fill amounts of jars of peanuts from a certain factors are known to follow a Normal distribution with mean 454g and standard deviation 15g. Suppose that a random sample of 60 jars is taken. What is the probability that the average weight of this sample is exactly 455g?

Select one:

a. 0.6030

b. Not enough information has been provided to answer the question.

c. 0.3970

d. 0.6985

e. 0.3015

f. 0.0000

A certain statistical test is designed so that it fails 2% of the time. Suppose that 700 of these tests are randomly selected, and we wish to calculate the proportion of these tests that result in a failure. What is the probability that less than 1% of these tests end in failure?

Select one:

a. 0.0588

b. 0.9412

c. 0.9706

d. We cannot reliably calculate this probability with the information given.

e. 0.0294

Answer 1

1)

sample size       =n=	1500
std error=σx̅=σ/√n=	0.0516

since sample size n>=30 ;

d. Approximately Normal with a mean of 24 months and a standard deviation of 0.0516 months.

2)

since point probability on a continuous distribution is zero:

f. 0.0000

3)

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.0200
sample size       =n=	700
std error of proportion=σp=√(p*(1-p)/n)=	0.0053

probability =P(X<0.01)=(Z<(0.01-0.02)/0.005)=P(Z<-1.8898)=0.0294

option E is correct